A pair of operator summation formulas and their applications

Authors:
Tian-Xiao He;Leetsch C. Hsu;Dongsheng Yin
Affiliations:
Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA;Department of Mathematics, Dalian University of Technology, Dalian 116024, PR China;College of Applied Sciences, Beijing University of Technology, Beijing 100022, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

Two types of symbolic summation formulas are reformulated using an extension of Mullin-Rota's substitution rule in [R. Mullin, G.-C. Rota, On the foundations of combinatorial theory: III. Theory of binomial enumeration, in: B. Harris (Ed.), Graph Theory and its Applications, Academic Press, New York, London, 1970, pp. 167-213], and several applications involving various special formulas and identities are presented as illustrative examples.